I agree with the rest of the folks who replied about proper tooling.  Using
the right tooling is important no mater what the finish of the PCB.  As far
as seeing problems with OSP boards, it may depend on what the finish is on
you connector.  Solder does act as a lubricant to aid in insertion.  If the
connector is solder coated then that issue goes away.  If it's gold plated
(or some other finish) then you may need to use a higher insertion force to
get the connector into an OSP board as opposed to a HAL or fused tin lead
board.  If you encounter trouble because of excessive insertion force
requirements you may be able to purchase the connector with a different
surface finish.  The connector vendor should be able to give you some idea
as to proper PCB hole dimensions (both drilled and finished) for each
surface finish.  These hole sizes and tolerances will be critical and may
not change because of surface finish.  The vendor should also be able to
tell you what insertion force is required.  This will most likely be a range
because of pin size and hole size tolerances.  Hope this helps.

Valquirio N. Carvalho